An extensive calibration of semi-empirical atmospheric density models (JR-71, MSIS-86, MSISE-90, TD-88) was carried out, by analyzing the orbital decay of nine spherical satellites in the 200-1500 km altitude range. The orbital decay data used spanned a full solar activity cycle (1987-1999). The drag coefficients obtained by fitting the observed semimaior axis evolution with a high accuracy orbit propagator were compared with those estimated by theoretical analysis. MSIS-86 and MSISE-90, practically identical above 200 km, resulted to be the best models to compute air density below 400 km, in low solar activity conditions. However, JR-71 seemed more precise at greater altitudes and/or solar activity. TD-88 gave quite mixed results, but generally closer to JR-71. The intrinsic accuracy of JR-71, MSIS-86 and MSISE-90 was generally better than 20%, often better than 15% and, sometimes, close to 10%. But at altitudes greater than 400 km this picture resulted progressively degraded. A better drag coefficient theory and dedicated laboratory measurements will be needed to investigate in detail the deficiencies of the current models and improve the knowledge of the earth atmosphere with satellite drag analysis.